API Reference¶

Divergence exports 79 public functions and 4 result types, organized into thematic modules.

Modules¶

Module	Description
Shannon Measures	Entropy, cross entropy, KL divergence, Jensen-Shannon, mutual information, joint and conditional entropy — both discrete and continuous
f-Divergences	General f-divergence engine plus TV, Hellinger, chi-squared, Jeffreys, and Cressie-Read
Rényi Family	Rényi entropy and divergence parameterized by order alpha
Integral Probability Metrics	Energy distance, Wasserstein, MMD, sliced Wasserstein
kNN Estimators	Kozachenko-Leonenko entropy, KSG mutual information, kNN KL divergence
Multivariate Dependence	Total correlation, normalized MI, variation of information
Causal / Temporal	Transfer entropy for directed information flow
Score-Based Measures	Fisher divergence and kernel Stein discrepancy (RBF + IMQ)
Sinkhorn Divergence	Debiased entropy-regularized optimal transport
Two-Sample Testing	Permutation tests with MMD, energy, and kNN statistics
Bayesian Diagnostics	ArviZ integration for MCMC convergence and inference diagnostics
Result Types	Named tuples returned by testing and diagnostic functions

Shorthand Aliases¶

For convenience, short aliases are provided for the most common measures. These dispatch to the unified _from_samples wrappers with a discrete toggle:

Alias	Equivalent to
`entropy()`	`entropy_from_samples()`
`cross_entropy()`	`cross_entropy_from_samples()`
`kl_divergence()`	`relative_entropy_from_samples()`
`jensen_shannon_divergence()`	`jensen_shannon_divergence_from_samples()`
`mutual_information()`	`mutual_information_from_samples()`
`joint_entropy()`	`joint_entropy_from_samples()`
`conditional_entropy()`	`conditional_entropy_from_samples()`

Plural aliases are also provided for the continuous functions that had singular names (e.g., continuous_entropy_from_samples = continuous_entropy_from_sample).

Common Parameters¶

Most functions accept these parameters:

base — Logarithm base controlling the unit of measurement: np.e (nats, default), 2 (bits), 10 (hartleys)
discrete — If True, use discrete estimators; if False (default), use continuous estimators
k — Number of nearest neighbors for kNN-based methods (default: 5)